Practice question

**Equipartition theorem** energy ½ k_B T per degree of freedom per molecule, f degrees give U = f/2 k_B T per molecule, f/2 R T per mole, internal energy function of T only for ideal gas, no intermolecular potential. P = (μ RT)/(V), P_HeP_O₂ = μ_Heμ_O₂.μ_He = (8)/(4) = 2 mol, μ_O₂ = (64)/(32) = 2 mol.Ratio = (2)/(2) = 1:1. Substituting values gives 1:1, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.